1. Cheap microfibers can swirl up paint but it shouldn't be THAT bad. As long as grit and dirt was not in the towels, they should be OK. Still, wash towels before you use them.
2. $10 says the car already had the swirls. They were just hidden. A lot of car dealer and detail shops uses waxes and stuff called "glaze" to shine the paint and hide defects like swirls. Now you have washed off the old crud and there they are. I've detailed 100's of new cars and almost all have some sort of swirl mark damage.
3. The material on a towel is the same as a mitt, so no reason to switch. The mitt holds more solution and can trap more dirt, but the microfiber material is pretty much the same.
25 yrs as a car detailer, I've seen a million hacked cars. Sad, really.